Answer
$2x^2y^2\sqrt[5] {y^3}$.
Work Step by Step
The given expression is
$\frac{\sqrt[5] {96x^{12}y^{11}}}{\sqrt[5] {3x^2y^{-2}}}$
Use the quotient rule $\frac{\sqrt[n] a}{\sqrt[n] b} = \sqrt[n] {\frac{a}{b}}$.
$=\sqrt[5] \frac{{96x^{12}y^{11}}}{ {3x^2y^{-2}}}$
Use $\frac{a^m}{a^n}=a^{m-n}$
$=\sqrt[5] {32x^{12-2}y^{11-(-2)}}$
$=\sqrt[5] {32x^{12-2}y^{11+2}}$
Simplify.
$=\sqrt[5] {32x^{10}y^{13}}$
Factor the radicand:
$=\sqrt[5] {2^5x^{5}x^5y^{5}y^5y^3}$
Simplify.
$=2xxyy\sqrt[5] {y^3}$
$=2x^2y^2\sqrt[5] {y^3}$.
